CAREER: Topological Abstraction for Robot Path Planning

高自由度机器人系统，如涉及一条或多条柔性电缆、多机器人系统、机器人机械手和软机械臂的系统，在自动化工业、家用机器人、医疗机器人、野外机器人和社会机器人中无处不在。多机器人系统可以使用电缆来拖曳或运输大型负载，机器人可以使用固定的系绳来供电或在GPS被拒绝的环境中执行长期任务。在隐私问题日益严重的社会政治环境中，多智能体系统需要新的创新来进行无协调规划。铰接式机器人应用于各种工业应用，如自动化制造，以及微创辅助腹腔镜手术。该学院早期职业发展(CALEAR)项目使用拓扑抽象技术解决了这类具有高维配置空间的系统降低复杂性的基本问题，目的是实现快速高效的规划。与该项目的研究目标相结合的是教育计划，旨在培训当代和未来一代工程师和研究人员，了解复杂自主系统的科学和技术，这些系统正日益成为我们现代社会的一部分。作为该项目的一个组成部分，STEM教育将通过建立一个包括研究生、本科生和K；12岁至12岁学生的指导生态系统来推进。来自代表性不足群体的学生将参与研究活动，目的是开发一个全面的、可扩展的教育计划。在这个项目中，将开发新的理论和算法工具来实现高维构形空间的拓扑抽象，目的是利用拓扑路径规划方法对高自由度系统进行高效的最优路径规划。同伦不变量将用于多个机器人在有障碍物的平面区域上导航的关节构形空间，从而降低了涉及系链多机器人系统、受限人-机器人团队以及大型无协调多智能体系统规划的复杂性。将开发新的算法来有效地计算空间域中的同伦不变量，从而导致与基于搜索的规划算法的直接融合，并应用于涉及电缆的空间系统。该项目超越了同伦，发展了对同伦概念的深入推广的理论基础，这将为发现和计算新的拓扑结构铺平道路，这种结构被称为Reeb结构，适用于关节机器人和软机器人的位形空间的降维。所有这些根本性的进步将允许开发高效的路径规划算法，并保证高自由度系统的完备性和最佳性，例如空间、多机器人系统和人-机器人系统，包括一根或多根柔性电缆；无协调多智能体系统；以及铰接式机械臂和可变形机械手。开发的算法将在真实的机器人平台上实施和评估。该项目由跨部门的机器人基础研究计划支持，该计划由工程总监(ENG)和计算机和信息科学与工程(CEISE)共同管理和资助。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

High degree-of-freedom robotic systems such as those involving one or more flexible cables, multi-robot systems, robotics manipulators and soft robotic arms, are ubiquitous in automation industries, household robotics, medical robotics, field robotics and social robots. Cables can be used by multi-robot systems to tug or transport large loads, and robots can use fixed tethers for power supply or communication for long-term missions in GPS-denied environments. Multi-agent systems need new innovations for coordination-free planning in a sociopolitical environment in which privacy concerns are on the rise. Articulated robotic manipulators are used in a variety of industrial applications such as automated manufacturing, as well as in minimally invasive assisted laparoscopic surgery. This Faculty Early Career Development (CAREER) project addresses the fundamental question of complexity reduction for such systems with high-dimensional configuration spaces using techniques of topological abstraction with an aim of achieving fast & efficient planning. Integrated with the research objectives of this project are educational plans aimed at training current and future generation of engineers & researchers in the science and technologies of complex autonomous systems that are increasingly becoming part of our modern society. As an integral part of the project, STEM education will be advanced through establishment of a mentoring ecosystem involving graduate, undergraduate & K-12 students. Students from underrepresented groups will be involved in the research activities with an aim of developing a comprehensive & scalable education program.In this project novel theoretical and algorithmic tools will be developed for achieving topological abstraction of high-dimensional configuration spaces with an aim of allowing efficient optimal path planning for high degree-of-freedom systems using Topological Path Planning methods. Homotopy invariants will be developed for joint configuration spaces of multiple robots navigating on planar domains with obstacles, resulting in complexity reduction in problems involving tethered multi-robot systems, constrained human-robot teams, and planning for large multi-agent systems without coordination. Novel algorithms for efficient computation of homotopy invariants in spatial domains will be developed, leading to direct amalgamation with search-based planning algorithms with application to spatial systems involving cables. The project goes beyond homotopy to develop the theoretical foundations of a deep generalization to the notion of homotopy, which will pave the way for the discovery and computation of novel topological constructions called Reeb structures that are suitable for dimensionality reduction of configuration spaces of articulated and soft robotic manipulators. All these fundamental advances will allow development of efficient path planning algorithms with completeness and optimality guarantees for high degree-of-freedom systems such as spatial, multi-robot systems & human-robot systems involving one or more flexible cables; coordination-free multi-agent systems; and articulated robotic arms & deformable manipulators. The developed algorithms will be implemented and evaluated on real robotic platforms.This project is supported by the cross-directorate Foundational Research in Robotics program, jointly managed and funded by the Directorates for Engineering (ENG) and Computer and Information Science and Engineering (CISE).This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.